Implications for intervention: Categorising the quantitative mental imagery of children

Unlike a child's observable, physical interactions with mathematical tools (e. g., physically touching blocks in order to count them), the subtle manifestations of imagery construction can be considerably more challenging to identify and act upon. Although there have been substantive examinations of mental imagery in a variety of mathematical contexts (i. e., spatial patterns, geometric rotation, etc.) there is a paucity of study regarding the nature of mathematical imagery with respect to initial counting acts. Towards that end, we conducted clinical interviews and longitudinal teaching experiments to ascertain the salient features of early quantitative mental imagery. Our findings indicate that children construct imagined units that are variably connected to the mathematical tool of the moment. Moreover, while this variability appears congruent with existing mathematical progressions, attending to nuances in children's mental imagery provides a platform for more refined instructional design. Indeed, identification of and attention to the child's quantitative imagery in whatever form it may take is essential to maximising mathematical experiences.